The overall goal of the proposed research is to develop mathematical and statistical models that can be used to interpret genetic data from human and nonhuman populations. Such models. are necessary to provided quantitative predictions of different genetic processes and to permit the statistical testing of hypotheses concerning mechanisms of genetic change. The proposed research will focus on five areas that are closely related in the kinds of data that will be analyzed and the kinds of mathematical methods that will be used. The areas are (a) geographic patterns in allele frequencies and DNA sequences, (b) tandemly repeated multigene families, (c) natural selection on guanine and cytocine content in the nuclear genome, (d) variation among nucleotide sites in substitution rates, and (e) genetics of clonally reproducing species. There will be particular emphasis on genetic changes caused by mutation, genetic drift, natural selection and gene flow at closely linked sites within a gene and at closely linked microsatellite loci. Microsatellite loci are associated with at least three genetic diseases in humans (fragile X syndrome, myotonic dystrophy, and Kennedy's disease) so it is especially important to understand the processes governing the distribution of allele sizes at such loci, which are found throughout the nuclear genomes of higher animals. A combination of analytic and computer simulation methods will be used in the proposed research. The analytic theory will provide the overall framework for understanding the processes modeled in each case and the computer simulation models will allow for the exploration of the robustness of the results obtained from the analytic models and will provide a way to test the statistical power of the methods developed. For models of selectively neutral alleles, most of the analytic theory will be based on the method of coalescents, in which the ancestry of genes or sites in a sample is modeled. Computer simulation models of neutral alleles will also be based on the coalescent approach.